Question

If f(x) = x³ – 15x² + 84x – 17, then ______.

विकल्प

• f(x) is decreasing in `(-oo, 10]` and increasing in `[10, oo)`

• f(x) is increasing in `(-oo, 10]` and decreasing in `[10, oo)`

• f(x) is increasing throughout real line

• f(x) is decreasing throughout real line

Answer 1

If f(x) = x³ – 15x² + 84x – 17, then f(x) is increasing throughout real line.

Explanation:

f(x) = x³ – 15x² + 84x – 17

⇒ f(x) = x³ – 15x² + 84x – 17

For f(x) to be increasing f'(x) > 0

⇒  3x² – 30x + 84 > 0

⇒ 3(x² – 10x + 25 + 3) > 0

⇒ 3[(x – 5)² + 3] > 0

Always increasing throughout real line.